Detailed Analysis of SCARA-Type Serial Manipulator on a Moving Base with LabView

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1 Internatonal Journal of Advanced Robotc Systems ARTICLE Detaled Analyss of SCARA-Type Seral Manpulator on a Movng Base wth LabVew Regular Paper Alrıa Kalel 1,*, Ahmet Dumlu 1, M. Fath Çorapsı 1 and Köksal Erentürk 1 1 Department of Electrcal and Electroncs Engneerng, Unversty of Ataturk, Turkey * Correspondng author E-mal: arakalel@gmal.com Receved 24 Sep 212; Accepted 19 Feb 213 DOI: / Kalel et al.; lcensee InTech. Ths s an open access artcle dstrbuted under the terms of the Creatve Commons Attrbuton Lcense ( whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. Abstract Robotc manpulators on a movng base are used n many ndustral and transportaton applcatons. In ths study, the modellng of a RRP SCARA type seral manpulator on a movng base s presented. A Lagrange Euler approach s used to obtan the complete dynamc model of the movng base manpulator. Hence, the dynamc model of the manpulator and the moble base are expressed separately. In addton, Vrtual Instrumentaton (VI) s developed for knematcs, dynamcs smulaton and anmaton of the manpulator combned wth the movngbase system. Usng the desgned VI n LabVew, the relatonshp between freuency of dsturbances of the movng base and ont torues s nvestgated. The obtaned results are presented n graphs. Keywords RRP Manpulator, Moble Base, Dynamc Model, Labvew, Smulaton 1. Introducton Robotc manpulators utled n many ndustral and transportaton applcatons, such as n underwater vehcles, space vehcles and surface shps, can be attached to movng bases. These manpulators are affected by dsturbances of the movng base. For example, manpulators attached to the surface of a shp are affected by the moton of the sea. Underwater vehcles are placed under addtonal forces produced by flow dynamcs and frctonal effects. The manpulators used n space research are affected by varable gravtatonal forces. These undesrable dsturbances have an mportant effect on moton and make t dffcult to control the manpulator [1, 2]. It s necessary to develop a complete dynamc model for robotc manpulators attached to a movng base n order to ncrease the ualty of control. For some applcatons, such as spray pantng, t s necessary to move the end effector of the manpulator along some desred paths wth prescrbed speed. To acheve ths goal, certan dynamcal euatons must be determned ncludng the parameters from the fxed base to the end effector. These euatons are applcable for fxed base manpulators, but we are oblged to adopt these euatons for movng base manpulators, too, n order to avod target trackng errors n the end effector. Therefore, the moton of the Alrıa Kalel, Ahmet Dumlu, Int J Adv M. Robotc Fath Çorapsı Sy, 213, and Vol. Köksal 1, 189:213 Erentürk: Detaled Analyss of SCARA-Type Seral Manpulator on a Movng Base wth LabVew 1

2 manpulator mounted on the movng base should be descrbed by a complete dynamc model. There are a lot of studes n the lterature whch take account of movng bases n dynamc modellng and control algorthms [3, 4, 5, 6]. A dynamc model of a 1 DOF robotc manpulator on a movng platform s presented n [7]. A dynamc model of a robotc manpulator base s derved n [8] and used for smulaton of a 2 DOF robot on a 3 DOF base. Computatonal methods to smulate a manpulator mounted on an underwater vehcle are presented n [9]. In ths paper, a SCARA RRP (Revolute Revolute Prsmatc), a manpulator wth three degrees of freedom, was mounted on a two degree of freedom moble base. Knematc analyss of the manpulator carred out frst by usng Denavt Hartenberg (D H) parameters. Then, the general dynamc model was developed for the manpulator and moble base usng a recursve method ncludng all of the parameters. These models of manpulator and moble base were obtaned by usng Lagrangan dynamcs and the Mathematca program, because of the complex structure of dynamc models. Fnally, the obtaned dynamc euatons were adapted n the LabVew program and the smulaton results were obtaned. Usng the LabVew envronment to smulate the consdered system wth the ad of the dynamc model derved s the man contrbuton of the present study. LabVew s a graphcal programmng language produced by Natonal Instrumentaton. It has been wdely adopted throughout ndustry and academa as a standard for nstrument control and data analyss smulaton software. LabVew also provdes scentsts and engneers wth nteractve programmng for system desgn and control. The advantage of utlng LabVew s that t provdes a powerful and flexble nstrumentaton and data analyss software system. LabVew not only helps renforce basc scentfc, mathematcal and engneerng prncples, but also allows communcaton wth the real world. The LabVew program conssts of two wndows, the front panel and the block dagram. The block dagram s the LabVew programmng code. Its large lbrares can be used to wrte a program. The front panel s an nterface of a desgned VI and ncludes knobs, swtches, meters, graphs, charts, etc. The LabVew program provdes an nteracton between supplyng nputs and observng outputs [1]. In ths study, a Vrtual Instrumentaton (VI) s bult for knematcs, dynamcs, smulaton and anmaton for supportng the manual calculaton of a three degree offreedom SCARA type robot and a two degree of freedom moble base. The desgned VI can smulate vsual movement of the SCARA robot and moble base. The organaton of the rest of the paper can be summared as follows: In secton 2 the modellng of a SCARA type manpulator robot wth three degrees of freedom s presented. General dynamc models of the manpulator and moble base are presented n secton 3. The desgned VI and smulaton results are dscussed n secton 4. Fnally, concludng remarks are gven n secton SCARA type Manpulator In general, a tradtonal SCARA type seral manpulator conssts of three nterconnected onts. These manpulators are commonly used n pck and place, assembly and packng applcatons n ndustry and transportaton [11, 12]. Especally when these manpulators are used n areas such as space exploraton and shppng, the degree of freedom of the manpulator s ncreased due to the movng base. Fg. 1 shows a schematc of a SCARA type manpulator and ts moble base. Fgure 1. Schematc of a SCARA type manpulator and moble base. 2.1 Knematcs analyss of manpulator In order to obtan the knematc model, we defne the below lsted frames, matrces and vectors as shown n Fgure 1. O: Fxed base frame attached on base of manpulator. I: Inertal base frame. A : Homogeneous transformaton matrx from th frame to th frame. I A : Homogeneous transformaton matrx from frame O to frame I. P : Poston vector of frame O relatve to frame I. ρ : Poston of pont on lnk relatve to frame. r : Poston of pont on lnk relatve to frame I. As shown n Fg. 1, the SCARA type manpulator has three onts whch are lnked to the robot. Jont 3 s a translatonal ont whch can move along the axs, whle 2 Int J Adv Robotc Sy, 213, Vol. 1, 189:213

3 onts 1 and 2 are rotatonal onts. For the coordnate systems shown n Fg. 1, the correspondng lnk parameters are lsted n Table 1. In addton, the parameters of the manpulator are tabulated n Table 2. Jont () a d 1 a1 d1 θ 1 2 π a2 θ 2 3 d3 Table 1. Denavt Hartenberg parameters of SCARA manpulator Symbol Descrpton Value a1 length of lnk1.325 m a2 length of lnk2.225m d1 length of lnk.55 m L length of lnk3.4 m m1 mass of lnk kg m2 mass of lnk kg m3 mass of lnk kg Table 2. Parameters of SCARA manpulator By applyng the homogeneous transformatons gven by E. (1), one obtans the knematc model gven by E. (2): A cos cossn snsn acos sn cos cos sn cos a sn 1 1 sn cos d A3 A A A (1) (2) It s necessary to descrbe the manpulator s fxed base frame poston and rotaton relatve to the nertal frame. Therefore, we should determne the end effector s poston and orentaton relatve to the nertal frame. By consderng the rotaton of the manpulator s base frame n relaton to the nertal frame, the homogeneous matrx can be stated as a rotaton of the frame about the XI axs by angle α, followed by a second rotaton of β about the YI axs and, addtonally, a constant translaton (P) along the XI axs by E. (3). cos sn sn cos sn Pcos I cos sn A sn sn cos cos cos Psn 1 3. General dynamc models of manpulator and moble base (3) After carryng out the knematc analyss of the manpulator we can obtan ts dynamc model by employng the Lagrange Euler formulaton based on the prncple of energy conservaton [13, 14]. If the 3 DOF SCARA type manpulator has three generaled coordnates and the moble base has n generaled coordnates, the total generaled coordnate of the system wll be (3+n) due to the nertal frame. In ths study, we assume that α and β are redundant coordnates; hence, the total generaled coordnate number of the system wll be eual to fve (=θ1, θ2, d3, α, β). The poston of a pont on the centre of mass of lnk relatve to the nertal frame s gven by E. (4): I O I r A A A.A (4) A : Ths matrx s a functon of the s(α, β) redundant generaled coordnate. I A O : Ths matrx s a functon of the ( 1, 2,d3) generaled coordnate. As each generaled coordnate s a tme functon, the velocty vector can be expressed as 2 I A I A r v A s A s 1 s 1 (5) The knetc energy for a sngle pont of mass, dm, can be defned as where tr s matrx trace. After substtutng E. (5): T 1 dk trr r dm 2 n I T 1 A T A I T dk tr A A s dm 2 s 1 1 s 1 n I T A T A I T tr A A dm s 2 s 1 1 s 1 n I T A T A tr A A I T dm s t 2 s 1 1 s n 1 I T A T A I T + tr 2 A A kdm s1 1 s The total knetc energy of the lnks s gven by ntegratng over the mass for each lnk and then summng as follows: n n L 1 K K dk (6) (7) (8) Alrıa Kalel, Ahmet Dumlu, M. Fath Çorapsı and Köksal Erentürk: Detaled Analyss of SCARA-Type Seral Manpulator on a Movng Base wth LabVew 3

4 n 2 I T A A I T KL tr A J A s 1s 1 1 s n 2 2 I I T 1 A T I T A tr A J A A s t 2 1s 1t 1 s t n T 1 I A A I T + tr A J A k 2 1 1k 1 k T The ntegral of the term over lnk s termed the pseudo nerta matrx J lnk T (9) dm (1) The potental energy of lnk s wrtten as I P m g A A (11) Knetc and potental energy euatons of the moble base are gven by E. (12): K tr J 2 2 I I T 1 A A s t 2 s 1t 1 s t I b P m g A b (12) Thus, the total knetc energy of the manpulator base system s wrtten as n 2 I T A A I T Ksysstem KL K tr A J A s 1s 1 1 s n 2 2 I I T 1 A T I T A tr A J A A s t 2 1s 1t 1 s t n T 1 I A A tr A I T J A k 2 1 1k 1 k 2 2 I T A A 1 / 2tr JO s t s1t1 s I I sstem b P P P m g A A m g A (13) 3.1 Lagrange Euler Formulaton The euatons of moton for a manpulator mounted on a moble platform are d L L dt p p (14) where p s the generaled coordnate and τ s the generaled force or torue at ont. Then, Lagrangan functon becomes n 2 I T A A I T L Ksystem Psystem tr A J A s 1s 1 1 s n 2 2 I I T 1 A T I T A tr A J A A s t 2 1s 1t 1 s (15) t n T 1 I A A tr A I T J A k 2 1 1k 1 k m I I ga bg A m A b Usng ths Lagrange functon and ts dervatve one may obtan the dynamc euatons for the manpulator mounted on a moble platform (E. 16): (16) p=1 gves the torue euaton for lnk 1; p=k gves the torue euaton for lnk k. Solutons of these moble manpulator euatons are performed wth Mathematca, and the dynamc euatons are transformed nto matrx form. Hence, the dynamc model of a manpulator and moble base can be expressed through E. (17): 1 2 H,, H, M C, G, (17) M: nerta matrx; C: vector of centrfugal and Corols Forces; G: vector of gravtatonal force; H 1 : smlar to nerta matrx based on poston, velocty and acceleraton vector of redundant generaled coordnate; H 2 : smlar to vector of centrfugal and Corols Forces based on poston and velocty vector of redundant generaled coordnate; : vector of generaled forces. 3.2 Platform Traectory For smplfcaton of the moble platform smulaton model, only roll and ptch moton wll be consdered. The followng type of dsturbance of the moble base s used to evaluate the model: 4 Int J Adv Robotc Sy, 213, Vol. 1, 189:213

5 Roll or ptch moton sne traectory 2 t t A sn( ) (18) T show dynamc behavour of the system for dfferent operatng ponts. 4. The desgned VI n LabVew and smulaton results where T s the perod, A s the ampltude and s the phase angle. As s well known from basc calculus, a snusod has dfferent slopes n all ponts of the graphcs. For ths reason, a snusodal traectory selecton wll be sutable to A graphcal soluton for calculatng, smulatng and anmatng the robot knematcs, dynamcs and movng s mplemented n a Vrtual Instrumentaton (VI) of LabVew. Usng the desgned VI, one can smulate and anmate onlne knematcs and dynamcs of SCARA type manpulators and dfferent types of dsturbances of the moble base. Fgure 2. LabVew front panel for RRP SCARA type manpulator Alrıa Kalel, Ahmet Dumlu, M. Fath Çorapsı and Köksal Erentürk: Detaled Analyss of SCARA-Type Seral Manpulator on a Movng Base wth LabVew 5

6 Fgure 3a. LabVew block dagram for RRP SCARA type manpulator (anmaton block) Fgure 3b. LabVew block dagram for RRP SCARA type manpulator (movng base traectory block) 6 Int J Adv Robotc Sy, 213, Vol. 1, 189:213

7 Fgure 3c. LabVew block dagram for RRP SCARA type manpulator (knematc and dynamc calculaton block) Fgures 2 and 3 show the desgned VI n a LabVew block dagram and the front panel for a RRP SCARA type manpulator on a movng base, respectvely. As shown n Fgures 2 and 3, the VI s used to move the manpulator by applyng mathematcal expresson of knematcs and dynamcs. To montor ont traectores, ont torues and movng base traectores, varous ndcators are located on the front panel. Ampltude, phase and perod knobs are used to set values for the roll and ptch of the movng base. In addton, the cubc and hgh order polynomal ont traectores optons and 3D anmaton screen are on the front panel. Fgure 4a. Traectores of ont 4.1 Smulaton results In order to examne the system, the cubc order polynomal ont traectores have been consdered. At the ntal locaton, the manpulator s assumed to be located at P1=[θ1=, θ2=, d3=]. For the fnal locaton, the manpulator moves from P1 to P2, located at P2=[θ1=2p/3 (rad), θ2=p/3 [rad], d3=.3 (m)] n 1 seconds. Frstly, nverse dynamc analyss of the SCARA type manpulator s smulated wthout takng nto consderaton dsturbance of the movng base. In the frst nstance, Roll and Ptch angles are both selected as. For ths case, ont traectory and actuatng torues of onts are presented n Fg. 4a, Fg. 4b and Fg. 4c. Fgure 4b. Actuaton torues for ont 1 and ont 2 (Roll&Ptch=) Fgure 4c. Actuaton torue for ont 3 (Roll&Ptch=) Alrıa Kalel, Ahmet Dumlu, M. Fath Çorapsı and Köksal Erentürk: Detaled Analyss of SCARA-Type Seral Manpulator on a Movng Base wth LabVew 7

8 In order to exhbt dynamc behavour of the system for dfferent operatng condtons, the second tral s dvded nto three subsectons. Three types of dsturbances of the moble base are used to evaluate the dynamc model. Frstly, t s assumed that the movng base rotates about the x axs wth a functon of sne as wrtten n E. (18) ( 2 t.5sn t, t ). The second assumpton 2.2 s that the movng base rotates smultaneously about the x and y axes wth a functon of sne as gven n E. (18) 2 2 ( t.5sn t, t.5sn t / 2 ). For these two consdered cases, actuatng torues of onts are presented Fgs. 5a, 5b, Fgs. 6a, 6b, respectvely. Fgure 6b. Actuaton torues for ont t.5sn t, t.5sn t / Fnally, n the thrd tral, the movng base rotates smultaneously about the x and y axes wth a hgher dsturbance freuency, as stated n E. (18) ( 2 2 t.5sn t, t.5sn t / 2 ). For.9.9 these cases, actuatng torues of onts are presented n Fgs. 7a and 7b, respectvely. Fgure 5a. Actuaton torues for ont 1 and ont 2 ( 2 t.5sn t, t ) 2.2 Fgure 7a. Actuaton torues for ont 1 and ont t.5sn t, t.5sn t / Fgure 5b. Actuaton torues for ont 3 2 t.5sn t, t ) 2.2 ( Fgure 7b. Actuaton torues for ont t.5sn t, t.5sn t / Fgure 6a. Actuaton torues for ont 1 and ont t.5sn t, t.5sn t / When Fgs. 5, 6 and 7 are compared wth Fg. 4, more snusodal oscllatons on the ont torues are observed, assocated wth ncreased freuency of roll and/or ptch dsturbances. As s well known, these oscllatons that have occurred on the ont torues affect the actuators of the manpulator as a dsturbance. When the freuency of 8 Int J Adv Robotc Sy, 213, Vol. 1, 189:213

9 dsturbance s further ncreased, performance of the manpulator wll decrease. The reason for ths decrease n performance s that achevable performance of the manpulator s lmted, n practce. The saturaton and flexblty effects are the man lmtatons. Not only the mechancal structure of the system, but also the mechancal tme constant of the used motor are therefore vtally mportant. 5. Conclusons Ths paper has presented a generc model of a robotc manpulator on a movng base. Knematcs and dynamcs euatons of the RRP SCARA type seral manpulator on a 2 DOF platform have been obtaned. The derved euatons have been smulated n the LabVew program. Inertal, Corols and centrfugal effects of the movng platform on the manpulator dynamcs have been nvestgated. It has been confrmed graphcally and numercally that redundant forces occur on the ont torues due to these effects. These forces cause devaton from the target traectory of the manpulator s end effector. Wth ths developed approach, t s shown that the dsturbance effects caused by the movng base can be added to the manpulator s dynamc model and expressed mathematcally. Also, when the freuency of dsturbance s ncreased, more snusodal oscllatons on the actuatng ont torues are observed. 6. Prelmnary expermental setup and future works The movement of a SCARA type manpulator can be observed usng a prelmnary expermental set up as shown n Fgure 8. Gyroscopes are physcal sensors that detect and measure the angular moton of an obect relatve to an nertal frame of reference. The roll and ptch angle values that are obtaned from the gyroscope sensor can be transferred to the computer usng a data acuston card (DAQ NI PCI 6259). Data acuston (DAQ) s the process of measurng an electrcal or physcal phenomenon wth a computer. A DAQ system conssts of sensors, DAQ measurement hardware, and a computer wth programmable software. In ths way, researchers can smultaneously observe ont torue varatons of ths manpulator and dsturbance of the moble base usng ths desgned VI n LabVew n real tme. Also, they can develop a model based control algorthm usng the obtaned complete dynamc model of SCARA type manpulators. The mnmum techncal reurements to ensure the ablty to run ths VI are tabulated n Table 3. Run Tme Engne Processor Pentum III/Celeron 866 MH or euvalent Development Envronment Pentum 4/M or euvalent RAM 256 MB 1 GB Screen 124 x 768 pxels 124 x 768 pxels Resoluton Operatng System Wndows 7/Vsta Wndows 7/Vsta (32 and 64 bt) (32 and 64 bt) Wndows XP SP3 Wndows XP SP3 (32 bt) (32 bt) Wndows Server 23 R2 Wndows Server 23 (32 bt) R2 (32 bt) Wndows Server 28 R2 Wndows Server 28 (64 bt) R2 (64 bt) Dsk Space 353 MB 3.67 GB (ncludes default drvers from NI Devce Drvers DVD) Table 3. Mnmum techncal reurements to run VI 7. References Fgure 8. Prelmnary expermental set up As shown n Fg. 8, the dsturbance effects on a manpulator base can be measured usng a gyroscope sensor (for example, a Sparkfun 6 DOF Inertal Measurng Unt). [1] From P J, Gravdahl T, Lllehagen T, Abbeel P (211). Moton plannng and control of robotc manpulators on seaborne platforms. Control Engneerng Practce,.19: [2] Wronka C M, Dunngan M W (211). Dervaton and analyss of a dynamc model of a robotc manpulator on a movng base. Robotcs and Autonomous Systems,.59: [3] Moharam H K, Rahm H N, Nkoobn A (212). Mathematcal modelng and traectory plannng of moble manpulators wth flexble lnks and onts. Appled Mathematcal Modellng..36: [4] Korayem M H, Gharblu H (23). Maxmum allowable load on wheeled moble manpulators Alrıa Kalel, Ahmet Dumlu, M. Fath Çorapsı and Köksal Erentürk: Detaled Analyss of SCARA-Type Seral Manpulator on a Movng Base wth LabVew 9

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